Seminar| Institute of Mathematical Sciences
Time: Friday, May 29th, 2026,14:00-15:00
Location: IMS R408
Speaker: Chongyao Chen, Stony Brook-USTC
Abstract:I will first explain how KNU’s completion theory—a generalization of toroidal compactifications—together with mirror symmetry allows us to complete the period map associated with a family of Calabi-Yau varieties, in a way that works even when the Mumford–Tate domain is non-Hermitian symmetric. I will then show how this completion, together with an analysis of limiting mixed Hodge structures and monodromy cones at distinguished boundary points, yields a method for computing the generic degree of the period map on a quasi-projective surface. As an application, I will show how the completion of the period map can be used to prove that the family satisfies the generic Torelli theorem—the Hodge structure determines the geometric shape up to finite ambiguity. The talk is based on my thesis and a joint work with Haohua Deng.